Implement up gate alternation dragging

- Grabbing a gate with alt held swiches to its alternate
- Alternate of control is anti-control, alternate of rotation is opposite rotation, etc
- Add 'alternate' property to Gate
- Specify alternates for existing gates
- Refactor 'silly' toolbox section into 'scalar'

src/circuit/Gate.js

@@ -173,6 +173,11 @@ class Gate {
          * @private
          */
         this._isDefinitelyUnitary = false;
+        /**
+         * The alternate gate for this one, used when shift+alt dragging.
+         * @type {!Gate}
+         */
+        this.alternate = this;
         /**
          * Returns context provided by this gate to other gates in the same column (or later columns in some cases).
          * @param {!int} qubit
@@ -235,22 +240,23 @@ class Gate {
      * @param {!string} name
      * @param {!string} blurb
      * @param {undefined|!string} serializedId
+     * @param {undefined|!Gate=} alternate
      * @returns {!Gate}
      */
-    static fromKnownMatrix(symbol, matrix, name='', blurb='', serializedId=undefined) {
+    static fromKnownMatrix(symbol, matrix, name='', blurb='', serializedId=undefined, alternate=undefined) {
         if (!(matrix instanceof Matrix)) {
             throw new DetailedError("Bad matrix.", {symbol, matrix, name, blurb});
         }
-        let g = new Gate();
-        g.symbol = symbol;
-        g.serializedId = serializedId === undefined ? symbol : serializedId;
-        g.name = name;
-        g.blurb = blurb;
-        g._isDefinitelyUnitary = matrix.isUnitary(0.01);
-        g._hasNoEffect = matrix.isIdentity();
-        g._stableDuration = Infinity;
-        g._knownMatrix = matrix;
-        return g;
+        let builder = new GateBuilder().
+            setSymbol(symbol).
+            setSerializedId(serializedId === undefined ? symbol : serializedId).
+            setTitle(name).
+            setBlurb(blurb).
+            setKnownEffectToMatrix(matrix);
+        if (alternate !== undefined) {
+            builder = builder.setAlternate(alternate);
+        }
+        return builder.gate;
     }
 
     /**
@@ -263,6 +269,7 @@ class Gate {
         g.symbol = this.symbol;
         g.name = this.name;
         g.blurb = this.blurb;
+        g.alternate = this.alternate;
         g.serializedId = this.serializedId;
         g.onClickGateFunc = this.onClickGateFunc;
         g.tag = this.tag;
@@ -489,6 +496,33 @@ class GateBuilder {
         return this;
     }
 
+    /**
+     * @param {!{all: !Array.<!Gate>, ofSize: !function(!int) : !Gate}} alternateFamily
+     * @returns {!GateBuilder}
+     */
+    setAlternateFromFamily(alternateFamily) {
+        return this.setAlternate(alternateFamily.ofSize(this.gate.height));
+    }
+
+    /**
+     * @param {!Gate} alternate
+     * @returns {!GateBuilder}
+     */
+    setAlternate(alternate) {
+        if (alternate === undefined) {
+            throw new Error("alternate === undefined");
+        }
+        if (alternate.height !== this.gate.height) {
+            throw new Error("alternate.height !== this.gate.height");
+        }
+        if (alternate.alternate !== alternate) {
+            throw new Error("alternate.alternate !== alternate");
+        }
+        alternate.alternate = this.gate;
+        this.gate.alternate = alternate;
+        return this;
+    }
+
     /**
      * Specifies the id to use when serializing/parsing this gate (instead of defaulting to the symbol).
      * @param {!string} serializedId

src/gates/AllGates.js

@@ -25,7 +25,12 @@ import {ErrorInjectionGate} from "src/gates/Debug_ErrorInjectionGate.js"
 import {ExponentiatingGates} from "src/gates/ExponentiatingGates.js"
 import {FourierTransformGates} from "src/gates/FourierTransformGates.js"
 import {HalfTurnGates} from "src/gates/HalfTurnGates.js"
-import {ImaginaryGate} from "src/gates/Joke_ImaginaryGate.js"
+import {
+    ImaginaryGate,
+    AntiImaginaryGate,
+    SqrtImaginaryGate,
+    AntiSqrtImaginaryGate
+} from "src/gates/Joke_ImaginaryGate.js"
 import {IncrementGates} from "src/gates/IncrementGates.js"
 import {InputGates} from "src/gates/InputGates.js"
 import {InterleaveBitsGates} from "src/gates/InterleaveBitsGates.js"
@@ -91,6 +96,9 @@ Gates.Exponentiating = ExponentiatingGates;
 Gates.FourierTransformGates = FourierTransformGates;
 Gates.HalfTurns = HalfTurnGates;
 Gates.ImaginaryGate = ImaginaryGate;
+Gates.AntiImaginaryGate = AntiImaginaryGate;
+Gates.SqrtImaginaryGate = SqrtImaginaryGate;
+Gates.AntiSqrtImaginaryGate = AntiSqrtImaginaryGate;
 Gates.IncrementGates = IncrementGates;
 Gates.InputGates = InputGates;
 Gates.InterleaveBitsGates = InterleaveBitsGates;
@@ -129,6 +137,9 @@ Gates.KnownToSerializer = [
     ZeroGate,
     NeGate,
     ImaginaryGate,
+    AntiImaginaryGate,
+    SqrtImaginaryGate,
+    AntiSqrtImaginaryGate,
 
     ...AmplitudeDisplayFamily.all,
     ...ProbabilityDisplayFamily.all,
@@ -250,14 +261,6 @@ Gates.TopToolboxGroups = [
             Detectors.XDetector, Detectors.XDetectControlClear,
         ]
     },
-    {
-        hint: 'Silly',
-        gates: [
-            ZeroGate,   MysteryGateMaker(),
-            NeGate,     ImaginaryGate,
-            SpacerGate, undefined,
-        ]
-    },
 ];
 
 /** @type {!Array<!{hint: !string, gates: !Array<undefined|!Gate>}>} */
@@ -332,6 +335,15 @@ Gates.BottomToolboxGroups = [
                 ModularMultiplicationGates.TimesInverseBToTheAModRFamily.ofSize(2),
         ]
     },
+    {
+        hint: 'Scalar',
+        gates: [
+            SpacerGate, ZeroGate,
+            NeGate, undefined,
+            ImaginaryGate, AntiImaginaryGate,
+            SqrtImaginaryGate, AntiSqrtImaginaryGate,
+        ]
+    },
 ];
 
 /** @type {!Map.<undefined|!string, !Array.<!Gate>>} */

src/gates/ArithmeticGates.js

@@ -53,6 +53,7 @@ ArithmeticGates.Legacy_AdditionFamily = Gate.buildFamily(2, 16, (span, builder)
     setKnownEffectToPermutation(chunkedScaledAdditionPermutationMaker(span, 1)));
 
 ArithmeticGates.Legacy_SubtractionFamily = Gate.buildFamily(2, 16, (span, builder) => builder.
+    setAlternateFromFamily(ArithmeticGates.Legacy_AdditionFamily).
     setSerializedId("sub" + span).
     setSymbol("b-=a").
     setTitle("Subtraction Gate").
@@ -76,6 +77,7 @@ ArithmeticGates.PlusAFamily = Gate.buildFamily(1, 16, (span, builder) => builder
     setKnownEffectToParametrizedPermutation((v, a) => (v + a) & ((1 << span) - 1)));
 
 ArithmeticGates.MinusAFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ArithmeticGates.PlusAFamily).
     setSerializedId("-=A" + span).
     setSymbol("−A").
     setTitle("Subtraction Gate [input A]").

src/gates/BitCountGates.js

@@ -47,6 +47,7 @@ BitCountGates.PlusBitCountAFamily = Gate.buildFamily(1, 16, (span, builder) => b
     setKnownEffectToParametrizedPermutation((t, a) => (t + Util.numberOfSetBits(a)) & ((1 << span) - 1)));
 
 BitCountGates.MinusBitCountAFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(BitCountGates.PlusBitCountAFamily).
     setSerializedIdAndSymbol("-cntA" + span).
     setSymbol("-1s(A)").
     setTitle("Bit Un-Count Gate").

src/gates/ComparisonGates.js

@@ -47,6 +47,7 @@ ComparisonGates.ALessThanB = new GateBuilder().
     gate;
 
 ComparisonGates.AGreaterThanB = new GateBuilder().
+    setAlternate(ComparisonGates.ALessThanB).
     setSerializedId("^A>B").
     setSymbol("⊕A>B").
     setTitle("Greater-Than Gate").
@@ -67,6 +68,7 @@ ComparisonGates.ALessThanOrEqualToB = new GateBuilder().
     gate;
 
 ComparisonGates.AGreaterThanOrEqualToB = new GateBuilder().
+    setAlternate(ComparisonGates.ALessThanOrEqualToB).
     setSerializedId("^A>=B").
     setSymbol("⊕A≥B").
     setTitle("At-Least Gate").
@@ -87,6 +89,7 @@ ComparisonGates.AEqualToB = new GateBuilder().
     gate;
 
 ComparisonGates.ANotEqualToB = new GateBuilder().
+    setAlternate(ComparisonGates.AEqualToB).
     setSerializedId("^A!=B").
     setSymbol("⊕A≠B").
     setTitle("Inequality Gate").

src/gates/Controls.js

@@ -37,6 +37,7 @@ Controls.Control = new GateBuilder().
     gate;
 
 Controls.AntiControl = new GateBuilder().
+    setAlternate(Controls.Control).
     setSerializedIdAndSymbol("◦").
     setTitle("Anti-Control").
     setBlurb("Conditions on a qubit being OFF.\nGates in the same column only apply to states meeting the condition.").
@@ -80,6 +81,7 @@ Controls.XAntiControl = new GateBuilder().
     gate;
 
 Controls.XControl = new GateBuilder().
+    setAlternate(Controls.XAntiControl).
     setSerializedId("⊖").  // The drawn +/- convention was changed, but the serialized id must stay the same.
     setSymbol("⊕").
     setTitle("X-Axis Control").
@@ -135,6 +137,7 @@ Controls.YAntiControl = new GateBuilder().
     gate;
 
 Controls.YControl = new GateBuilder().
+    setAlternate(Controls.YAntiControl).
     setSerializedId("(/)").  // The drawn cross/slash convention was changed, but the serialized id must stay the same.
     setSymbol("⊗").
     setTitle("Y-Axis Control").

src/gates/CountingGates.js

@@ -133,6 +133,7 @@ CountingGates.CountingFamily = Gate.buildFamily(1, 16, (span, builder) => builde
     setKnownEffectToTimeVaryingPermutation((t, i) => offsetPermutation(t, +1, span, i)));
 
 CountingGates.UncountingFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(CountingGates.CountingFamily).
     setSerializedId("Uncounting" + span).
     setSymbol("-⌈t⌉").
     setTitle("Down Counting Gate").

src/gates/CycleBitsGates.js

@@ -83,6 +83,7 @@ CycleBitsGates.CycleBitsFamily = Gate.buildFamily(2, 16, (span, builder) => buil
     setKnownEffectToBitPermutation(i => (i + 1) % span));
 
 CycleBitsGates.ReverseCycleBitsFamily = Gate.buildFamily(2, 16, (span, builder) => builder.
+    setAlternateFromFamily(CycleBitsGates.CycleBitsFamily).
     setSerializedId(">>" + span).
     setSymbol(">>>").
     setTitle("Right Rotate").

src/gates/ExponentiatingGates.js

@@ -45,6 +45,7 @@ ExponentiatingGates.XForward = new GateBuilder().
     gate;
 
 ExponentiatingGates.XBackward = new GateBuilder().
+    setAlternate(ExponentiatingGates.XForward).
     setSerializedIdAndSymbol("e^iXt").
     setTitle("X-Exponentiating Gate (backward)").
     setBlurb("Left-hand rotation around the X axis.\nPasses through ±iX instead of X.").
@@ -63,6 +64,7 @@ ExponentiatingGates.YForward = new GateBuilder().
     gate;
 
 ExponentiatingGates.YBackward = new GateBuilder().
+    setAlternate(ExponentiatingGates.YForward).
     setSerializedIdAndSymbol("e^iYt").
     setTitle("Y-Exponentiating Gate (backward)").
     setBlurb("Left-hand rotation around the Y axis.\nPasses through ±iY instead of Y.").
@@ -81,6 +83,7 @@ ExponentiatingGates.ZForward = new GateBuilder().
     gate;
 
 ExponentiatingGates.ZBackward = new GateBuilder().
+    setAlternate(ExponentiatingGates.ZForward).
     setSerializedIdAndSymbol("e^iZt").
     setTitle("Z-Exponentiating Gate (backward)").
     setBlurb("Left-hand rotation around the Z axis.\nPasses through ±iZ instead of Z.").

src/gates/FourierTransformGates.js

@@ -89,6 +89,7 @@ FourierTransformGates.FourierTransformFamily = Gate.buildFamily(1, 16, (span, bu
 FourierTransformGates.InverseFourierTransformFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
     setSerializedId("QFT†" + span).
     setSymbol("QFT^†").
+    setAlternateFromFamily(FourierTransformGates.FourierTransformFamily).
     setTitle("Inverse Fourier Transform Gate").
     setBlurb("Transforms from/to phase frequency space.").
     setActualEffectToUpdateFunc(ctx => applyBackwardGradientShaders(ctx, span)).

src/gates/IncrementGates.js

@@ -19,6 +19,7 @@ IncrementGates.IncrementFamily = Gate.buildFamily(1, 16, (span, builder) => buil
     setKnownEffectToPermutation(t => (t + 1) & ((1 << span) - 1)));
 
 IncrementGates.DecrementFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(IncrementGates.IncrementFamily).
     setSerializedId("dec" + span).
     setSymbol("−1").
     setTitle("Decrement Gate").

src/gates/InterleaveBitsGates.js

@@ -124,6 +124,7 @@ InterleaveBitsGates.InterleaveBitsGateFamily = Gate.buildFamily(4, 16, (span, bu
     setKnownEffectToBitPermutation(b => interleaveBit(b, span)));
 
 InterleaveBitsGates.DeinterleaveBitsGateFamily = Gate.buildFamily(4, 16, (span, builder) => builder.
+    setAlternateFromFamily(InterleaveBitsGates.InterleaveBitsGateFamily).
     setSerializedId("split" + span).
     setSymbol("Deinterleave").
     setTitle("Deinterleave").

src/gates/Joke_ImaginaryGate.js

@@ -28,4 +28,39 @@ const ImaginaryGate = new GateBuilder().
     setKnownEffectToMatrix(Matrix.square(Complex.I, 0, 0, Complex.I)).
     gate;
 
-export {ImaginaryGate}
+const AntiImaginaryGate = new GateBuilder().
+    setAlternate(ImaginaryGate).
+    setSerializedIdAndSymbol("-i").
+    setTitle("Anti-Imaginary Gate").
+    setBlurb("Phases everything by -i.").
+    setDrawer(args => {
+        GatePainting.paintLocationIndependentFrame(args);
+        GatePainting.paintGateSymbol(args);
+    }).
+    setKnownEffectToMatrix(Matrix.square(Complex.I.neg(), 0, 0, Complex.I.neg())).
+    gate;
+
+const SqrtImaginaryGate = new GateBuilder().
+    setSerializedIdAndSymbol("√i").
+    setTitle("Half Imaginary Gate").
+    setBlurb("Phases everything by √i.").
+    setDrawer(args => {
+        GatePainting.paintLocationIndependentFrame(args);
+        GatePainting.paintGateSymbol(args);
+    }).
+    setKnownEffectToMatrix(Matrix.square(1, 0, 0, 1).times(new Complex(Math.sqrt(0.5), Math.sqrt(0.5)))).
+    gate;
+
+const AntiSqrtImaginaryGate = new GateBuilder().
+    setAlternate(SqrtImaginaryGate).
+    setSerializedIdAndSymbol("√-i").
+    setTitle("Half Anti-Imaginary Gate").
+    setBlurb("Phases everything by √-i.").
+    setDrawer(args => {
+        GatePainting.paintLocationIndependentFrame(args);
+        GatePainting.paintGateSymbol(args);
+    }).
+    setKnownEffectToMatrix(Matrix.square(1, 0, 0, 1).times(new Complex(Math.sqrt(0.5), -Math.sqrt(0.5)))).
+    gate;
+
+export {AntiImaginaryGate, ImaginaryGate, SqrtImaginaryGate, AntiSqrtImaginaryGate}

src/gates/ModularAdditionGates.js

@@ -50,6 +50,7 @@ ModularAdditionGates.PlusAModRFamily = Gate.buildFamily(1, 16, (span, builder) =
     setKnownEffectToParametrizedPermutation((t, a, r) => t < r ? (t + a) % r : t));
 
 ModularAdditionGates.MinusAModRFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ModularAdditionGates.PlusAModRFamily).
     setSerializedId("-AmodR" + span).
     setSymbol("−A\nmod R").
     setTitle("Modular Subtraction Gate").

src/gates/ModularIncrementGates.js

@@ -63,6 +63,7 @@ ModularIncrementGates.IncrementModRFamily = Gate.buildFamily(1, 16, (span, build
     setKnownEffectToParametrizedPermutation((t, a) => t < a ? (t + 1) % a : t));
 
 ModularIncrementGates.DecrementModRFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ModularIncrementGates.IncrementModRFamily).
     setSerializedId("decmodR" + span).
     setSymbol("−1\nmod R").
     setTitle("Modular Decrement Gate").

src/gates/ModularMultiplicationGates.js

@@ -226,6 +226,7 @@ ModularMultiplicationGates.TimesAModRFamily = Gate.buildFamily(1, 16, (span, bui
     setKnownEffectToParametrizedPermutation(modularMultiply));
 
 ModularMultiplicationGates.TimesAModRInverseFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ModularMultiplicationGates.TimesAModRFamily).
     setSerializedId("/AmodR" + span).
     setSymbol("×A^-1\nmod R").
     setTitle("Modular Division Gate").
@@ -253,6 +254,7 @@ ModularMultiplicationGates.TimesBToTheAModRFamily = Gate.buildFamily(1, 16, (spa
     setKnownEffectToParametrizedPermutation((t, a, b, r) => modularPowerMultiply(t, b, a, r)));
 
 ModularMultiplicationGates.TimesInverseBToTheAModRFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ModularMultiplicationGates.TimesBToTheAModRFamily).
     setSerializedId("/BToAmodR" + span).
     setSymbol("×B^-A\nmod R").
     setTitle("Modular Power Division Gate").

src/gates/ModularMultiplyAccumulateGates.js

@@ -60,6 +60,7 @@ ModularMultiplyAccumulateGates.PlusABModRFamily = Gate.buildFamily(1, 16, (span,
     setKnownEffectToParametrizedPermutation((t, a, b, r) => t < r ? (t + a*b) % r : t));
 
 ModularMultiplyAccumulateGates.MinusABModRFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(ModularMultiplyAccumulateGates.PlusABModRFamily).
     setSerializedId("-ABmodR" + span).
     setSymbol("−AB\nmod R").
     setTitle("Modular Multiply-Subtract Gate").

src/gates/MultiplicationGates.js

@@ -62,6 +62,7 @@ MultiplicationGates.TimesAFamily = Gate.buildFamily(1, 16, (span, builder) => bu
     setKnownEffectToParametrizedPermutation((x, a) => modularMultiply(x, a, 1<<span)));
 
 MultiplicationGates.TimesAInverseFamily = Gate.buildFamily(1, 16, (span, builder) => builder.
+    setAlternateFromFamily(MultiplicationGates.TimesAFamily).
     setSerializedId("/A" + span).
     setSymbol("×A^-1").
     setTitle("Inverse Multiplication Gate").